where \(\mathbf {U},\mathbf {V}\)  are obtained from the singular value
decomposition of \((\mathbf {\breve{V}}_{{\color {black}k}}^{\dagger }\mathbf {Q}\mathbf {\breve{V}}_{{\color {black}k}})^{-1/2}\dot{\mathbf {H}}_{{\color {black}k}}^{\dagger }\) 
[1]}. In light of AO algorithm
in [2]}, [3]}, [4]}, we first fix
\(\mathbf {Q}\)  and consider the following problem
\(\begin{array}{rl}{\operatornamewithlimits{maximize}} & \sum _{k=1}^{K}\log |\mathbf {\breve{V}}_{k}^{\dagger }\mathbf {Q}^{n}\breve{\mathbf {V}}_{k}+\dot{\mathbf {H}}_{k}^{\dagger }\bar{\mathbf {S}}_{k}\dot{\mathbf {H}}_{k}|\\\operatornamewithlimits{subject~to}& \sum _{k=1}^{K}\operatorname{tr}(\bar{\mathbf {S}}_{k})=P;\lbrace \bar{\mathbf {S}}_{k}\succeq \mathbf {0}\rbrace .\end{array}\) 
